When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

There is a pressing need for edible delivery systems to encapsulate, protect, and release bioactive lipids within the food, medical, and pharmaceutical industries. The fact that these delivery systems must be edible puts constraints on the type of ingredients and processing operations that can be used to create them. Emulsion technology is particularly suited for the design and fabrication of delivery systems for encapsulating bioactive lipids. This review provides a brief overview of the major bioactive lipids that need to be delivered within the food industry (for example, ω-3 fatty acids, carotenoids, and phytosterols), highlighting the main challenges to their current incorporation into foods. We then provide an overview of a number of emulsion-based technologies that could be used as edible delivery systems by the food and other industries, including conventional emulsions, multiple emulsions, multilayer emulsions, solid lipid particles, and filled hydrogel particles. Each of these delivery systems could be produced from food-grade (GRAS) ingredients (for example, lipids, proteins, polysaccharides, surfactants, and minerals) using simple processing operations (for example, mixing, homogenizing, and thermal processing). For each type of delivery system, we describe its structure, preparation, advantages, limitations, and potential applications. This knowledge can be used to facilitate the selection of the most appropriate emulsion-based delivery system for specific applications.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1750-3841.2007.00507.x

Emulsion-based delivery systems for lipophilic bioactive components.

The past 20 years have witnessed ever-growing evidence that the mechanical properties of biological tissues, from nanoscale to macroscale dimensions, are fundamental for cellular behaviour and consequent tissue functionality. This knowledge, combined with previously known biochemical cues, has greatly advanced the field of biomaterial development, tissue engineering and regenerative medicine. It is now established that approaches to engineer biological tissues must integrate and approximate the mechanics, both static and dynamic, of native tissues. Nevertheless, the literature on the mechanical properties of biological tissues differs greatly in methodology, and the available data are widely dispersed. This Review gathers together the most important data on the stiffness of living tissues and discusses the intricacies of tissue stiffness from a materials perspective, highlighting the main challenges associated with engineering lifelike tissues and proposing a unified view of this as yet unreported topic. Emerging advances that might pave the way for the next decade’s take on bioengineered tissue stiffness are also presented, and differences and similarities between tissues in health and disease are discussed, along with various techniques for characterizing tissue stiffness at various dimensions from individual cells to organs. The complexity of biological tissue presents a challenge for engineering of mechanically compatible materials. In this Review, the stiffness of tissue components — from extracellular matrix and single cells to bulk tissue — is outlined, and how this understanding facilitates the engineering of materials with lifelike properties is discussed.

/pdf/the-stiffness-of-living-tissues-and-its-implications-for-49xikp5kk1.pdf

The stiffness of living tissues and its implications for tissue engineering

Food proteins: a review on their emulsifying properties using a structure-function approach.

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.

/pdf/dynamical-boson-stars-2qp0jhfpoi.pdf

Dynamical boson stars

By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing feature of this class of solutions is that they admit a linear equation of state which can be applied to strange stars with quark matter.

A class of relativistic stars with a linear equation of state

We find a class of solutions to the Einstein–Maxwell system for a charged sphere with a particular choice of the electric field intensity by assuming a particular form for the hypersurfaces {t = constant}. In the uncharged limit we regain static stars studied previously. A qualitative analysis of the physical features of the model is performed. The presence of charge allows for more general behaviour than is the case for uncharged spheres. In particular we show that the causal signals are permitted over a wider range of parameters in the presence of charge. Also we show that our solutions satisfy a simple scaling relationship.

General Solution for a Class of Static Charged Spheres

The singularity free space-time metric obtained by Krori and Barua (J. Phys. A, Math. Gen. 8:508, 1975) satisfies the physical requirements of a realistic star. Consequently, we explore the possibility of applying the Krori and Barua model to describe ultra-compact objects like strange stars. For it to become a viable model for strange stars, bounds on the model parameters have been obtained. Consequences of a mathematical description to model strange stars have been analyzed.

Strange stars in Krori-Barua space-time

Influence of transglutaminase treatment of skim milk on the formation of ε-(γ-glutamyl)lysine and the susceptibility of individual proteins towards crosslinking

We propose a model for an anisotropic dark energy star where we assume that the radial pressure exerted on the system due to the presence of dark energy is proportional to the isotropic perfect fluid matter density. We discuss various physical features of our model and show that the model satisfies all the regularity conditions and is stable as well as singularity-free.

Ranjan Sharma

Papers

A class of relativistic stars with a linear equation of state

General Solution for a Class of Static Charged Spheres

Strange stars in Krori-Barua space-time

Influence of transglutaminase treatment of skim milk on the formation of ε-(γ-glutamyl)lysine and the susceptibility of individual proteins towards crosslinking

Singularity-free dark energy star